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Calculate (A) the Trapezoidal Approximation and (B) Simpson's Approximation To \int

Question 172

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Calculate (a) the trapezoidal approximation and (b) Simpson's approximation to ∫abf(x)dx\int _ { a } ^ { b } f ( x ) d x where f is the tabulated function. xa=1.01.331.672.02.332.673.0=bf(x)5.26.91.40.062.30.011.5\begin{array} { l r l l l l l l } \mathrm { x } & \mathrm { a } = 1.0 & 1.33 & 1.67 & 2.0 & 2.33 & 2.67 & 3.0 = \mathrm { b } \\\hline \mathrm { f } ( \mathrm { x } ) & 5.2 & 6.9 & 1.4 & 0.06 & 2.3 & 0.01 & 1.5 \\\hline\end{array} Enter your answers in that order as just unlabeled real numbers rounded off to two decimal places, separated by a comma.

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